How bright the moon: correcting a propagated figure error in the literature

How bright the moon: correcting a propagated figure error in the literature

Last year, the National Park Service released our report, Artificial night lighting and protected lands: Ecological effects and management approaches (Longcore and Rich 2016), which had been in the works for quite a while. Our colleague Andrej Mohar, while enthusiastic about the report overall, pointed out that a figure that we had included of natural illumination under various conditions was wrong, and by quite a bit, when it came to the levels under a “quarter moon.”  This is the story of that error, where it came from, and its correction.

The figure we used in the 2016 NPS report was re-printed with very minor adjustments from Paul Beier’s chapter in our 2006 edited book, Ecological Consequences of Artificial Night Lighting (Island Press).


This figure was published in Ecological Consequences of Artificial Night Lighting and re-published with slight adjustment of the icons in our 2016 NPS report.

The “quarter moon” is shown as causing ground-based illumination of 0.1 lux or thereabouts.  This is obviously and very wrong, and in fact is contradicted in Chapter 1 of the book, which indicates 0.01-0.03 lux for a quarter moon. We should have caught it then, but did not.

Furthermore, a quarter moon, technically, is half of the disk of the moon illuminated, which is one quarter of the entire moon. The icon we used for the “quarter moons” in the figure, however, is that of a crescent moon, with closer to one quarter of the disk  illuminated. We had switched the icon for the “quarter moons” from a depiction of three quarters of the disk illuminated to one quarter of the disk illuminated to match this commonsense language.

Beier (2006) had adapted the graphic from McFarland et al. (1999), who cited their sources as Blaxter (1970) and Brown (1952).  It was McFarland et al. (1999) who introduced the error.  They correctly copied the illumination line from a moon with three-quarters of the face illuminated (a gibbous moon) and incorrectly labeled it as “quarter moons.” They  had three-quarters of the face illuminated in the icon, which was correct, but inconsistent with the label.


 Illuminations produced by the sun and moon as reported by McFarland et al. (1999). Note that “quarter moons” identifies the same line as a three-quarter moon in Brown (1952) once the conversion from footcandles to lux is made.

Compare the figure from McFarland et al. (1999) with the figure produced by Brown for the Department of Navy in 1952. The Brown figure is in footcandles.


Illumination produced by the phases of the moon reported by Brown (1952). The text “1st and 3rd Quarters” indicates the “apparent half moon.”

The 1952 Brown report provides curves of illumination from the moon at four phases: full (phase angle 0º), three-quarters full (phase angle 60º), half full (phase angle 90º, which is technically a “quarter moon”) and one-quarter full (phase angle 120º). In the McFarland et al. (1999) diagram, two curves are given: one for the full moon and one for “quarter moons.” The full moon line is correct. The “quarter moons” line is the same as the three-quarters full moon in Brown (1952), meaning that the lunar disk is three-quarters illuminated (phase angle 60º) and not a “quarter moon” in the sense of one quarter of the disk being illuminated or even a quarter moon meaning one quarter of the entire moon visible and illuminated (half of the disk visible and illuminated).

Unfortunately, this error propagated forward to Beier (2006), our 2016 report (which is being reissued with a corrected figure), and Gaston et al. (2014), who changed the icon to a crescent moon (as we did in our report) and might have shifted the line down slightly, but not enough to be accurate, especially given the icon depiction of a crescent moon and textual description.



Illumination from the sun and moon reported by Gaston et al. (2014). The curve for the “quarter moons” is shifted downward slightly but is an order of magnitude higher than a crescent moon (a quarter of the face illuminated) and higher than a quarter moon (half of the face illuminated).

I regret not catching the error when editing Beier’s chapter or when updating the figure in 2016. But Andrej did catch it and now the record can be set straight.


This corrected version of the figure shows maximum values for a full moon (0.3 lux) and quarter moons (0.03 lux) with the proper icon for quarter moon showing half of the face illuminated.

For the record, the approximate values for the maximum clear-sky illumination from the moon directly overhead at its phases are as follows.


Phase Angle

Brown (1952) (lux)

(Krisciunas & Schaefer 1991) (lux)

100% illuminated



75% illuminated




First and Last Quarter
50% illuminated




25% illuminated




These values can vary based on the distance between the sun and the moon and whether the moon is waxing or waning because of the differing characteristics of the face of the moon. Illuminations this high are unlikely to occur under most circumstances, especially at temperate latitudes. A working estimate of illumination from the full moon is closer to 0.1 lux on the ground than the ~0.4 lux potential maximum illumination, a fact that has been recently discussed by Kyba et al. (2017).

Travis Longcore, Ph.D.
August 5, 2017

Literature Cited

Beier, P. 2006. Effects of artificial night lighting on terrestrial mammals. Pages 19–42 in C. Rich, and T. Longcore, editors. Ecological consequences of artificial night lighting. Island Press, Washington, D.C.

Blaxter, J. H. S. 1970. Light, Animals, Fishes. Pages 213–230 in O. Kinne, editor. Marine ecology: a comprehensive integrated treatise on life in oceans and coastal waters. Wiley-Interscience, London.

Brown, D. R. 1952. Natural illumination charts. Research and Development Project NS 714-100. Pages 1–11, 43 plates. Department of the Navy, Bureau of Ships, Washington, D.C.

Gaston, K. J., J. P. Duffy, S. Gaston, J. Bennie, and T. W. Davies. 2014. Human alteration of natural light cycles: causes and ecological consequences. Oecologia 176:917–931.

Krisciunas, K., and B. E. Schaefer. 1991. A model of the brightness of moonlight. Publications of the Astronomical Society of the Pacific 103:1033–1039.

Kyba, C., A. Mohar, and T. Posch. 2017. How bright is moonlight? Astronomy & Geophysics 58:1.31–31.32.

Longcore, T., and C. Rich. 2016. Artificial night lighting and protected lands: Ecological effects and management approaches. Natural Resource Report NPS/NRSS/NSNS/NRR—2016/1213. National Park Service, Fort Collins, Colorado.

McFarland, W., C. Wahl, T. Suchanek, and F. McAlary. 1999. The behavior of animals around twilight with emphasis on coral reef communities. Pages 583–628 in S. N. Archer, M. B. A. Djamgoz, E. R. Loew, J. C. Partridge, and S. Vallerga, editors. Adaptive mechanisms in the ecology of vision. Kluwer Academic Publishers, Dordrecht.


CubeSats to measure light pollution

CubeSats to measure light pollution

I had the fortune of being able to offer some examples of environmental applications in a paper by Dee Pack and Brian Hardy from Aerospace Corporation for the Small Satellite Conference this summer in Utah.  We (mostly they) show the feasibility of using small satellites to measure upward radiance from Earth at night, with examples ranging from the Middle East to Southern California.  I’m glad to have offered the concept of “darkest path” modeling for wildlife connectivity and perspectives on the usefulness of spectral information at this scale. The work we have been doing with the VIIRS Day-Night Band shows up for the identification of a very bright greenhouse on the Oxnard Plain.  Here is the citation, abstract, and download link.

Pack, D. W., B. S. Hardy, and T. Longcore. 2017. Studying Earth at night from CubeSats. Proceedings of the 31st Annual AIAA/USU Conference on Small Satellites, Leo Missions, SSC17-WK-35.

This paper presents examples of the latest imaging data of the Earth at night from multiple CubeSat platforms. Beginning in 2012, with AeroCube-4, The Aerospace Corporation has launched multiple CubeSat platforms in different orbits equipped with a common suite of CMOS sensors. Originally designed as utility cameras to assist with attitude control system studies and star sensor development, we have been using these simple camera sensors to image the Earth at night since 2014. Our initial work focused on observing nighttime urban lights and global gas flare signals at higher resolution than is possible with the VIIRS sensor. To achieve optimum sensitivity and resolution, orbital motion is compensated for via the use of on-board reaction wheels to perform point-and-stare experiments, often with multiple frame exposures as the sensor moves in orbit. Ground sample distances for these systems range from approximately 100 to 130 meters for the narrow-field-of-view cameras, to 500 meters for the medium-field-of-view cameras. In our initial work, we demonstrated that CMOS sensors flown on AeroCube satellites can achieve a nighttime light detection sensitivity on the order of 20 nW-cm-2-sr-1. This resolution and sensitivity allows for detection of urban lighting, road networks, major infrastructure illumination, natural gas flares, and other phenomena of interest. For wide-area surveys, we can also program our cameras to observe regions of interest and co-add pixels to reduce the data bandwidth. This allows for a greater number of frames to be collected and downloaded. These results may then be used to task later satellite passes. Here, we present new examples of our nighttime Earth observation studies using CubeSats. These include: 1) detecting urban growth and change via repeat imaging, 2) investigating the utility of color observations, 3) spotting major sources of light pollution, 4) studying urban-wildland interface regions where lighting may be important to understanding wildlife corridors, 5) imaging lightning and cloud cover at night using wide-area imaging, 6) observations of the very bright lights of fishing boats, and 7) observing other interesting natural phenomenon, including airglow emissions, and the streaking caused by proton strikes in the South Atlantic Anomaly. Our ongoing work includes utilizing a diversity in overpass times from multiple satellites to observe nighttime scenes, imaging high-latitude cities not optimally accessed by the international space station’s cameras, and building a catalogue of observations of rapidly developing megacities and global infrastructure nodes. Data from CMOS sensors flown in common on 5 different AeroCubes in 4 different orbits have been collected. Our results show that enhanced CubeSat sensors can improve mapping of the human footprint in targeted regions via nighttime lights and contribute to better monitoring of: urban growth, light pollution, energy usage, the urban-wildland interface, the improvement of electrical power grids in developing countries, light-induced fisheries, and oil industry flare activity. Future CubeSat sensors should be able to contribute to nightlights monitoring efforts by organizations such as NOAA, NASA, ESA, the World Bank and others, and offer low-cost options for nighttime studies.

Spatial and Temporal Analysis of Nighttime Lighting In and Around National Parks


Yu Chuan Shan, Ben Banet, and I have been working the past couple of years on developing a monthly database of upward radiance from within and buffers around all of the National Park units in the United States.  They are presenting the research today at the USC undergraduate research symposium.  The results presented only scratch the surface of what we can do to analyze this high-resolution database over space and time.

Shan also put together a website to walk through the project.

The poster can be downloaded here. Please cite as:

Shan, Yu Chuan, Ben Banet, and Travis Longcore. 2017. Spatial and Temporal Analysis of Nighttime Lighting In and Around National Parks. USC Undergraduate Symposium for Scholarly and Creative Work (Los Angeles, April 12, 2017).

Healthy Urbanism in Polluted Cities



Colleagues at USC Environmental Health Centers are putting together a 1-day conference titled Parks, Pollution, and Obesity. I’ve been awarded a USC Architecture Graduate Research Scholar grant to work with this group to bridge between the public health researchers and landscape architects and urbanists. The premise is as follows.

Awareness among landscape architects, urban designers, and urbanists of the need for green spaces to promote physical activity and combat obesity is high and provision of recreational opportunities in park-poor communities is perceived as an unmitigated good. The adverse health consequences of breathing polluted air is likewise well known, but generally assumed to apply to respiratory diseases such as asthma and lung cancer. Recent research, however, has documented that exposure to air pollution can result directly in increased propensity for obesity, through exposure to particulates and chemicals that disrupt metabolism and promote fat accumulation (McConnell et al. 2016). Air pollution is also linked epidemiologically with diabetes and cardiovascular disease. Urbanists therefore face a challenge of balancing the benefits of a landscape that promotes activity and provides green space in park-poor neighborhoods, and the adverse impacts of exposure to air pollution, which is exacerbated during exercise. Planners and designers need high-quality information to guide location and attributes of green spaces if the benefits are to outweigh the harms.

MLA student Nina Mross will be working with us as a Graduate Research Scholar to review the efforts made within landscape architecture and urbanism to address air quality concerns, describe case studies of such efforts, and illustrate the best practices that arise from the April conference.


McConnell, R., F. Gilliland, M. Goran, H. Allayee, A. Hricko, and S. Mittelman. 2016. Does near-roadway air pollution contribute to childhood obesity? Pediatric Obesity 11:1–3.

Invasion of the Earthworms

Invasion of the Earthworms

Image: San Clemente Island by Shishir Paudel

Many of the species of earthworms in North America are exotic species and their presence alters native ecosystems in profound ways that resonate from the soil up through the vegetation and into the vertebrate communities.  So when word came that the US Navy had found earthworms on San Clemente Island, an island thought to be earthworm free, and was looking for an assessment of their distribution and possibilities for eradication I was interested.

I contacted earthworm (and bird) expert Scott Loss at Oklahoma State and we were able to secure the funding.  He put together a team that included post-doc Shishir Paudel and other colleagues at Oklahoma State and Beau MacDonald (at first UWG contract GIS expert and now USC Spatial Sciences Institute staff GIS Project Specialist) did the GIS work and modeling on our end.  The second of the papers from the study came out this week in Diversity and Distributions and Beau put together this summary graphic.


Source: Beau MacDonald, graphical summary of Paudel, S., G.W.T. Wilson, B. MacDonald, T. Longcore, and S. R. Loss. Predicting spatial extent of invasive earthworms on an oceanic island. Diversity and Distributions (2016).

The bottom line is that the earthworms (several species of them) were found near the main road and in areas that were moist.  All of the best-performing predictive models for the distribution of the earthworm included proximity to the paved road.  This suggests that the invasion is in its early stages and is associated with the road in some way.

We speculate, but do not have proof, that the earthworms were introduced when topsoil was brought from the mainland in 2008-2009 to pave the road.  This explanation is consistent our team not finding any earthworms south of the southernmost extent of the paving (the dashed line in the middle map above).

The paper goes into detail about the vegetation conditions where the earthworms were found; they are associated with exotic grasses and other non-native plants.

Time will tell the full effect of the invasion of earthworms on San Clemente Island.  The island has remarkable archeological resources because it used to be free of burrowing animals that moved soil and artifacts around. Being earthworm free (and free of burrowing mammals) was an advantage for those resources in addition to being the natural ecological condition.  I hope this research provides a warning to those proposing and doing construction on oceanic islands with high biological diversity and natural values to sterilize any building materials being imported for use lest they introduce unexpected species to environments where they can do damage.

Paudel, S., G.W.T. Wilson, B. MacDonald, T. Longcore, and S. R. Loss. Predicting spatial extent of invasive earthworms on an oceanic island. Diversity and Distributions (2016).



Invasions of non-native earthworms into previously earthworm-free regions are a major conservation concern because they alter ecosystems and threaten biological diversity. Little information is available, however, about effects of earthworm invasions outside of temperate and boreal forests, particularly about invasions of islands. For San Clemente Island (SCI), California (USA) – an oceanic island with numerous endemic and endangered plant and vertebrate species – we assessed the spatial extent and drivers of earthworm invasion and examined relationships between earthworms and plant and soil microbial communities.


San Clemente Island, southern California, USA.


Using a stratified random sampling approach, we sampled earthworms, vegetation, soils and microbial communities across SCI. We examined the relationship between the presence of invasive earthworms and soil and landscape variables using logistic regression models and implemented a spatial representation of the best model to represent potential site suitability for earthworms. We evaluated the relationship between invasive earthworms and vegetation and microbial variables using ANOVA.


We found that the likelihood of encountering earthworms increased close to roads and streams and in high moisture conditions, which correspond to higher elevation and a north-eastern aspect on SCI. The presence of earthworms was positively associated with total ground vegetation cover, grass cover and non-native plant cover; however, there was no significant relationship between earthworms and microbial biomass. These results suggest that the earthworm invasion on SCI is at an early stage and closely tied to roads and high moisture conditions.

Main conclusions

Climatic variables and potential sources of earthworm introduction and dispersal (e.g. roads and streams) should be broadly useful for predicting current and future sites of earthworm invasions on both islands and continents. Furthermore, the significant positive relationship between non-native plant cover and invasive earthworm presence raises the possibility of an emerging invasional ‘meltdown’ on SCI. Additional study of earthworm invasions on human-inhabited oceanic islands is necessary to identify additional invasions and their potential for negative impacts on unique insular biota.

Unintentional Media Blitz

As a result of the new atlas of of artificial night sky brightness I ended up doing a lot of interviews for national and international outlets, including Science Magazine,, Christian Science Monitor, Scientific American, and USA Today.

Then the American Medical Association released a statement on LED lighting (for which I had provided some background information) and a few more stories came out in and Christian Science Monitor.

A couple of Los Angeles Times stories also happened to include me:

Rare toads (presumably) love him; off-roaders do not 

The sunset that takes an hour to go from date palms to to redwoods

Predicting Continental-Scale Bird Migration Routes from Landscape Parameters

William Winters, one of my GIST students, successfully filed his MS thesis last fall, in which he created proof-of-concept models for bird migration routes at the continental scale.  We developed the topic as a way to fill in a missing scale in the efforts to reduce mortality of birds at towers and buildings.  At the scale of the building and tower, mitigations are now available, including lights-out during migration, and changing the lighting scheme on towers.  But what locations are most likely to have high levels of birds during migration, outside those already known as migratory hotspots (e.g., Cape May)?

Put another way, what places on the landscape are especially bad for tall towers and buildings because they are likely to kill more birds?  Are there really fewer birds killed at obstructions in the western part of the Great Plains as the records in our 2012 PLoS ONE paper might suggest?

Residuals in tower height-mortality regression at communication towers (Longcore et al. 2012).

Residuals in tower height-mortality regression at communication towers (Longcore et al. 2012). Note that the towers along the Front Range of the Rockies killed fewer birds than expected.

I posed the question of whether one could model probable migratory routes using least-cost path analysis and a simple set of physical parameters for sets of known wintering and breeding grounds for Neotropical migrant birds.  William ran with it.

A least-cost corridor raster for Red-eyed Vireos migrating from the Northern Atlantic forest to South America.

A least-cost corridor raster for Red-eyed Vireos migrating from the Northern Atlantic forest to South America (Winters 2015).

After some careful thinking about resolution and projection, William settled upon topography (slope) as a metric of landscape resistance, along with wind and an additional resistance value for crossing the Gulf of Mexico. Then, using pairs of wintering and breeding grounds for Red-eyed Vireo, Kirtland’s Warbler, and Golden-cheeked Warbler, he developed models to predict northbound and southbound migration routes.

The resulting maps, which were the result of some experimentation and comparison with existing observations compiled for the species in the literature and on eBird provide proof-of-concept that one could develop maps for whole species by linking together known wintering and breeding grounds.

Fall and Spring migration routes predicted for Kirtland's Warbler from Michigan only.

Fall migration route predicted for Kirtland’s Warbler from Michigan only (Winters 2015).

The maps show that the least-cost paths for the spring and fall migrations might be different.  For example, the models for Red-eyed Vireos southbound from New England funnel through the Florida Peninsula in the Fall, and return via the Gulf Coast of Florida in the Spring.

To see the full thesis, including many more maps, visit the USC Library website at this link: Identifying areas of high risk for avian mortality by performing a least accumulated-cost analysis.

Belowground interactions with aboveground consequences: Invasive earthworms and arbuscular mycorrhizal fungi

Shishir Paudel, Travis Longcore, Beau MacDonald, Melissa K. McCormick, Katalin Szlavecz, Gail W. T. Wilson,  and Scott R. Loss


Volume 97, Issue 3, March 2016, Pages 605–614

Abstract.  A mounting body of research suggests that invasive nonnative earthworms substantially alter microbial communities, including arbuscular mycorrhizal fungi (AMF). These changes to AMF can cascade to affect plant communities and vertebrate populations. Despite these research advances, relatively little is known about (1) the mechanisms behind earthworms’ effects on AMF and (2) the factors that determine the outcomes of earthworm–AMF interactions (i.e., whether AMF abundance is increased or decreased and subsequent effects on plants). We predict that AMF-mediated effects of nonnative earthworms on ecosystems are nearly universal because (1) AMF are important components of most terrestrial ecosystems, (2) nonnative earthworms have become established in nearly every type of terrestrial ecosystem, and (3) nonnative earthworms, due to their burrowing and feeding behavior, greatly affect AMF with potentially profound concomitant effects on plant communities. We highlight the multiple direct and indirect effects of nonnative earthworms on plants and review what is currently known about the interaction between earthworms and AMF. We also illustrate how the effects of nonnative earthworms on plant–AMF mutualisms can alter the structure and stability of aboveground plant communities, as well as the vertebrate communities relying on these habitats. Integrative studies that assess the interactive effects of earthworms and AMF can provide new insights into the role that belowground ecosystem engineers play in altering aboveground ecological processes. Understanding these processes may improve our ability to predict the structure of plant and animal communities in earthworm-invaded regions and to develop management strategies that limit the numerous undesired impacts of earthworms.

Heading to New Orleans: Ecologically Sensitive Lighting Design

Landscape architects, mark your calendars.  I’ll be part of a joint presentation on Ecologically Sensitive Lighting Design that was just accepted to the American Society of Landscape Architects annual meeting in New Orleans this fall.  I teamed up with lighting designer Linnaea Tillett and lighting engineer Nancy Clanton, two of the top landscape lighting experts in the country on the session proposal.  We will use a case study format to explore approaches to landscape lighting (and not lighting…) that incorporate the psychology of place-making, consideration for nature, and technical advances in the field.

Boulder City Hall lighting design by Clanton and Associates.

Boulder City Hall lighting design by Clanton and Associates.